Divide the polynomials. The form of your answer should either be $p(x)$ or $p(x)+\dfrac{k}{x-5}$ where $p(x)$ is a polynomial and $k$ is an integer. $\dfrac{2x^3-11x^2+25}{x-5}=$
Solution: Usually, there are many different ways to divide polynomials. Here, we will use the method of polynomial long division. Notice that the expression in the numerator is missing a $1^{\text{st}}$ degree term. To avoid any confusion, let's add that term as $0x$. $\begin{array}{r} 2x^2-\phantom{1}x-\phantom{1}5 \\ x-5|\overline{2x^3-11x^2+0x+25} \\ \mathllap{-(}\underline{2x^3-10x^2\phantom{+0x+25}\rlap )} \\ -x^2+0x+25 \\ \mathllap{-(}\underline{-x^2+5x\phantom{+25}\rlap )} \\ -5x+25 \\ \mathllap{-(}\underline{-5x+25\rlap )} \\ 0 \end{array}$ We found that the quotient is $2x^2-x-5$ and the remainder is $0$, which means the answer is simply a polynomial (no expression of the form $\dfrac{k}{x-5}$ ). $\dfrac{2x^3-11x^2+25}{x-5}=2x^2-x-5$